Algebra: Solving Equations and Inequalities

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Questions and Answers

What is the value of x in the equation $-(1 - x) = -2(3x - 1)$?

1/7

3/5

3/7 (correct)

1/5

If $-5x + 7 = 2x - 3$, what is the value of x?

4/3

4/7

10/3

10/7 (correct)

What is the solution for n in the inequality $-17 + 3n ≤ 7(n - 2)$?

n ≤ 15/4 (correct)

n ≥ 15/4

n ≥ 3/4

n ≤ -3/4

Which point is on the graph of $2x - 16y = 8$?

(0, 2) Signup and view all the answers

Solving the area formula $A = 1/2 (b₁ + b₂)h$ for $b₁$ results in which equation?

b₁ = 2A/h - b₂ Signup and view all the answers

From the profit equation $P = 2n - 800$, express n as a function of P.

n = 1/2 (P + 800) Signup and view all the answers

Which inequality could be used to determine b, the number of blouses, and p, the number of pants that Grace can afford?

17b + 25p ≤ 75 Signup and view all the answers

In the given right triangle, which system of equations could be used to solve for x and y if y is 15 less than twice x?

x + y = 90; 2x - y = 15 Signup and view all the answers

What is the maximum number of hamburgers Harry can buy if he buys 20 hot dogs?

38 hamburgers Signup and view all the answers

Which of the following represents a function based on the given set of ordered pairs?

{(7, 4), (8, 4), (9, 4), (9, 5)} Signup and view all the answers

What is the range of the function represented by the given temperature vs. time graph?

All real numbers between and including 50 and 212. Signup and view all the answers

Based on the graph modeling price markup, which option correctly describes the function's domain?

Numbers between and including 0 and 36. Signup and view all the answers

What is the total bill a homeowner must pay for using 3800 gallons of water, considering both water and sewer fees?

$33.25 Signup and view all the answers

What is the weight of a baby at age 5 months according to the function f(x) = 1.5x + 7?

13.5 pounds Signup and view all the answers

What is the value of the function f(x) = 5(x + 1) + 2x at x = 3?

16 Signup and view all the answers

Which of the following pairs represents a function based on the given criteria?

{(0, 1), (1, 2), (2, 3), (3, 4)} Signup and view all the answers

What is the correct domain for the profit function P(t) of the math club selling T-shirts, where each T-shirt sold represents a profit of $2?

0 ≤ t ≤ 500 Signup and view all the answers

In the context of the lava flow modeled by the function f(d) = 800d, what is the best description of the domain?

All non-negative integers. Signup and view all the answers

What does an average change in distance of zero imply about Victoria's movements between 10:00 a.m. and 11:00 a.m.?

Victoria could have stayed at the same location from 10:00 a.m. to 11:00 a.m. Signup and view all the answers

How is the average rate of change for the function f(x) calculated over the interval [1, 8] given specific values?

(f(8) - f(1)) / (8 - 1) Signup and view all the answers

When calculating the average rate of change in miles per gallon from 180 miles to 480 miles, which values are used in the expression?

480 - 180 / 300 Signup and view all the answers

Which of the following statements about the distance and time table for Victoria is accurate?

Victoria's distance returned to 0 miles indicates she returned home. Signup and view all the answers

What does the slope of the line represented in the graph from (0,0) to (5,5) signify?

The relationship is linear with a slope of 1. Signup and view all the answers

Which range of values can correctly be described as the domain of the function P(t), where t represents the number of T-shirts sold?

t must be between 0 and 500, inclusive. Signup and view all the answers

Study Notes

Solving Equations and Inequalities

Question 1: The value of x in the equation -(1 - x) = -2(3x - 1) is 1/7.
Question 2: If -5x + 7 = 2x - 3, then x = 10/7.
Question 3: The solution for n in the inequality -17 + 3n ≤ 7(n - 2) is n ≥ 15/4*.
Question 4: The point (1/2, 0) is on the graph of 2x -16y = 8.

Trapezoids and Formulas

Question 5: The formula A = 1/2 (b₁ + b₂)h can be used to determine the area of a trapezoid. Solving for b₁ will result in the equation b₁ = 2A/h - b₂.
Question 6: The equation P = 2n - 800 can be rearranged to solve for n as a function of P resulting in the following: n = 1/2 (P + 800)
Question 7: The formula C = (5n + 40)/9 can be rearranged to solve for the number of chirps as a function of the temperature in degrees Celsius. The correctly rearranged formula is n = 9/5 (C - 40)*.

Inequalities and Systems of Equations

Question 8: The inequality 17b + 25p ≤ 75 could be used to determine b, the number of blouses, and p, the number of pants Grace can afford.
Question 9: The system of equations x + y = 90* and 2x - y = 15 could be used to solve for x and y.

Word Problems

Question 10: A possible way Harry might buy the hamburgers and hot dogs is 66 hamburgers and 33 hot dogs.
Question 11: The set of ordered pairs {(-4, 4), (-2, 4), (1, 4), (5, 4)} represents a function.

Functions

Question 12: The range of the function shown in the graph is All real numbers between and including 50 and 212.
Question 13: Based on the given graph, the function's domain is Numbers between and including 0 and 30.
Question 14: The total amount a homeowner will pay if the water and sewer usage for one month is 3800 gallons is $43.35.
Question 15: According to the model f(x) = 1.5x + 7, the weight of a baby at age 5 months is 14.5 pounds.
Question 16: Given f(x) = 5(x + 1) + 2x, f(3) is 26.
Question 17: The domain of the function shown in the graph is All real numbers between 0 and 6.
Question 18: A reasonable domain of the function P(t) is 0 ≤ t ≤ 500.
Question 19: The domain of f(d) in the context of the lava flow is best described as All non-negative integers.
Question 20: The best interpretation of Victoria's average change in distance during this time is Victoria could have stayed at the same location from 10:00 a.m. to 11:00 a.m..

Rate of Change

Question 21: The average rate of change for the function f(x) over the interval [1, 8] is 4.
Question 22: The average rate of change, in miles per gallon, from 180 miles to 480 miles is 480 - 180 / 300.

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Description

This quiz focuses on solving equations and inequalities, including their graphical interpretations and applications in trapezoid area calculations. Test your skills with varied problems, ranging from basic equations to more complex algebraic manipulations.